不变的集合和准确答案(1+ 2 ) 维的波浪方程被讨论。在那里存在，这被显示出属于不变的集合 E <SUB>0</SUB>= 的方程的答案的一个类 { u：u <SUB > x </SUB>= v <SUB > x </SUB > F (u) ， u <S...不变的集合和准确答案(1+ 2 ) 维的波浪方程被讨论。在那里存在，这被显示出属于不变的集合 E <SUB>0</SUB>= 的方程的答案的一个类 { u：u <SUB > x </SUB>= v <SUB > x </SUB > F (u) ， u <SUB > y </SUB>= v <SUB > y </SUB > F (u)} 。这条途径也被开发解决(1 + N ) 维的波浪方程。展开更多
<正> In this paper,we introduce a new invariant set _0={u:u_x=f'(x)F(u)+ε[g'(x)-f'(x)g(x)]F(u)×exp(-i∫~u 1/F(z) dz)},where f and g are some smooth functions of x,ε is a constant,and F is a sm...<正> In this paper,we introduce a new invariant set _0={u:u_x=f'(x)F(u)+ε[g'(x)-f'(x)g(x)]F(u)×exp(-i∫~u 1/F(z) dz)},where f and g are some smooth functions of x,ε is a constant,and F is a smooth function to bedetermined.The invariant sets and exact solutions to nonlinear diffusion equation u_t=(D(u)u_x)_x+Q(x,u)u_x+P(x,u),are discussed.It is shown that there exist several classes of solutions to the equation that belong to the invariant set _0.展开更多
With the (k,n) -threshold scheme of secret sharing in the field of information security technology asan application background,the concept of set ( k,n)-exact cover is presented in this paper.It is a modificationof th...With the (k,n) -threshold scheme of secret sharing in the field of information security technology asan application background,the concept of set ( k,n)-exact cover is presented in this paper.It is a modificationof the original concept of set covering problem.It is also different from the concept of exact coverdefined by J.E.Hopcroft.Some properties of ( k,n) -exact cover are investigated;a sufficient conditionfor a set to be ( k,n ) -exactly coverable is given.It follows that a feasible assignment scheme of a set forthe (k,n) -exact cover is obtained if this set satisfies the sufficient condition.展开更多
First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction ...First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.展开更多
In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.
We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson construct...We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos.10447007 and 10671156Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘不变的集合和准确答案(1+ 2 ) 维的波浪方程被讨论。在那里存在，这被显示出属于不变的集合 E <SUB>0</SUB>= 的方程的答案的一个类 { u：u <SUB > x </SUB>= v <SUB > x </SUB > F (u) ， u <SUB > y </SUB>= v <SUB > y </SUB > F (u)} 。这条途径也被开发解决(1 + N ) 维的波浪方程。
基金National Natural Science Foundation of China under Grant Nos.10472091,10332030 and 10502042the Natural Science Foundation of Shanxi Province under Grant No.2003A03
基金National Natural Science Foundation of China under Grant Nos.10472091,10332030,and 10502042the Natural Science Foundation of Shaanxi Province under Grant No.2003A03
文摘<正> In this paper,we introduce a new invariant set _0={u:u_x=f'(x)F(u)+ε[g'(x)-f'(x)g(x)]F(u)×exp(-i∫~u 1/F(z) dz)},where f and g are some smooth functions of x,ε is a constant,and F is a smooth function to bedetermined.The invariant sets and exact solutions to nonlinear diffusion equation u_t=(D(u)u_x)_x+Q(x,u)u_x+P(x,u),are discussed.It is shown that there exist several classes of solutions to the equation that belong to the invariant set _0.
基金Supported by the National Natural Science Foundation of China (No. 60673053 90718011 )
文摘With the (k,n) -threshold scheme of secret sharing in the field of information security technology asan application background,the concept of set ( k,n)-exact cover is presented in this paper.It is a modificationof the original concept of set covering problem.It is also different from the concept of exact coverdefined by J.E.Hopcroft.Some properties of ( k,n) -exact cover are investigated;a sufficient conditionfor a set to be ( k,n ) -exactly coverable is given.It follows that a feasible assignment scheme of a set forthe (k,n) -exact cover is obtained if this set satisfies the sufficient condition.
基金Supported by the National Natural Science Foundation of China (10371092)the Foundation of Wuhan University
文摘First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.
基金supported by the National Natural Science Foundation of China(10371092)Foundation of Ningbo University(8Y0600036).
文摘In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.
文摘We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;
